Body torque/couple

Figure 274(a) depicts the drive system which was already part of the earliest machines (see Figure 225). More recent machines, instead of powering shaft (3) by transmission belts, apply a motor (5) with a torque-limiting clutch, a gear reducer (4), and a flexible coupling to drive gear shaft (3) mounted in or on the roller press frame. The gear on shaft (3) transmits torque to the coupled gears (2) on the roll shafts between two roller bodies (1).

Another parameter of interest for comparison with experimental measurements is the couple or torque on a particle arising from rotational motion. The torque T about the center of rotation of a body with angular velocity to can be written in Cartesian tensor form as... 

Descriptive Statistics (e.g., mean, median, variance, standard deviation) Hypothesis Testing (e.g., paired and un-paired t-tests chi-squared test) Principles of Statics (e.g., forces moments couples torques free-body diagrams)... 

In some way, this coupling of two models by residual sinks may be compared to the temporary coupling of two bodies such as the plates of a clutch by a residual sink (cf. Fig. 2.15). As long as the clutch is disengaged, there is no force acting between the two plates. If, however, the clutch engages, a torque acts on both of them such that the difference of their angular velocities is zero. The load side is forced to adapt to drive side. This approach has been applied for the numerical computation of ARR residuals from continuous time models [14, 17] and recently also to systems described by a hybrid model [18]. 

Couple k3-p3l couple of if often k9-pl9 [ME, pair, bond, ff. OF cople, ff. L copula bond, fr. co- + apere to fasten] (13c) n. Two equal and oppositely directed parallel but not coUinear forces acting upon a body to form a couple. The moment of the couple or torque is given by the product of one of the forces by the perpendicular distance between them. Dimension [M L T j. 

In mechanics of rotation, the force F acting at a distance R from a center around which a body can rotate corresponds to a state variable T from the family of efforts called torque (or couple). All these variables are oriented in space and therefore represented by vectors. The relationship between force and torque is expressed by a vector product of the distance (radius of gyration) by the force... 

So far we have introduced four Miesowicz viscosities. Two other viscosities can be proposed by considering the following. The director n in Fig. 4.1(a), if free to move, will rotate due to a viscous torque the viscosity coefficient 71 is introduced to describe this situation and characterises the torque associated with a rotation of n. For this reason 71 is often called the rotational viscosity or twist viscosity. The coefficient 71 generally determines the rate of relaxation of the director. Also, a rotation of n due to body forces will induce a flow. The viscosity coefficient 72 characterises the contribution to the torque due to a shear velocity gradient in the nematic and is sometimes referred to as the torsion coefficient in the velocity gradient it leads to a coupling between the orientation of the director and shear flow. The two viscosities 71 and 72 have no counterpart in isotropic fluids. We therefore have a total of six viscosities four Miesowicz viscosities plus 71 and 72. It turns out, as will be seen in the problems to be discussed in later Sections, that 7i and 72 are precisely the viscosities introduced in the constitutive theory at equations (4.78) and (4.79), namely. 

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